Question

A distance of 150 km was covered by a motorcyclist traveling at an average speed of 75 km/h, by a bus at 60 km/h, a truck at 50 km/h, and a bicyclist at 20 km/h. How much time did each require to travel the entire distance? Explain why speed and the time needed to travel 150 km are inversely proportional quantities?

I need to know how to explain the last sentence.

Answer 1

Motorcyclist: 2 hours

Bus: 2.5 hours

Truck: 3 hours

Bicyclist: 7.5 hours

Explanation:

Answer 2

Part 1) It took the motorcyclist 2 hours to cover the entire distance.

Part 2) It took the bus 2.5 hours to cover the entire distance.

Part 3) It took the truck 3 hours to cover the entire distance.

Part 4) It took the bicyclist 7.5 hours to cover the entire distance.

Part 5) The explanation in the procedure

Explanation:

we know that

The speed is the ratio between the distance and the time

Let

s -----> speed in km/h

d ----> distance in km

t ----> the time in hours

so

`s=(d)/(t)`

Part 1) A distance of 150 km was covered by a motorcyclist traveling at an average speed of 75 km/h

How much time did each require to travel the entire distance?

we have

`d=150\ km`

`s=75\ km/h`

substitute in the formula and solve for t

`75=(150)/(t)`

`t=(150)/(75)`

`t=2\ h`

therefore

It took the motorcyclist 2 hours to cover the entire distance.

Part 2) A distance of 150 km was covered by a bus traveling at an average speed of 60 km/h

How much time did each require to travel the entire distance?

we have

`d=150\ km`

`s=60\ km/h`

substitute in the formula and solve for t

`60=(150)/(t)`

`t=(150)/(60)`

`t=2.5\ h`

therefore

It took the bus 2.5 hours to cover the entire distance.

Part 3) A distance of 150 km was covered by a truck traveling at an average speed of 50 km/h

How much time did each require to travel the entire distance?

we have

`d=150\ km`

`s=50\ km/h`

substitute in the formula and solve for t

`50=(150)/(t)`

`t=(150)/(50)`

`t=3\ h`

therefore

It took the truck 3 hours to cover the entire distance.

Part 4) A distance of 150 km was covered by a bicyclist traveling at an average speed of 20 km/h

How much time did each require to travel the entire distance?

we have

`d=150\ km`

`s=20\ km/h`

substitute in the formula and solve for t

`20=(150)/(t)`

`t=(150)/(20)`

`y=7.5\ h`

therefore

It took the bicyclist 7.5 hours to cover the entire distance.

Part 5) Explain why speed and the time needed to travel 150 km are inversely proportional quantities?

we know that

A relationship between two variables, x, and y, represent an inverse variation if it can be expressed in the form
`y*x=k` or
`y=k/x`

In this problem

the constant k will be the distance d

the variable y will be the speed s

the variable x will be the time t

so

speed and time are inversely proportional quantities because

when speed increases -------> the time decreases

when speed decreases -------> the time increases